Continuous-Time Enclosures for Uncertain Implicit Differential Equations

doi:10.1016/j.ifacol.2015.08.163

	Continuous-Time Enclosures for Uncertain Implicit Differential Equations
	Rayjaguru, Jai 1; Villanueva, Mario E.1; Houska, Boris2 ; Chachuat, Benoit 1
	2015
会议录名称	IFAC PAPERSONLINE
卷号	48
期号	8
页码	94-99
发表状态	已发表
DOI	10.1016/j.ifacol.2015.08.163
摘要	The computation of enclosures for the reachable set of uncertain dynamic systems is a crucial component in a wide variety of applications, from global and robust dynamic optimization to safety verification and fault detection. Even though many systems in engineering are best modeled as implicit differential equations (IDEs) and differential algebraic equations (DAEs), methods for the construction of enclosures for these are not as well developed as they are for ordinary differential equations (ODEs). In this paper, we propose a continuous-time approach for the guaranteed over approximations of the reachable set for quasilinear IDEs. This approach builds on novel high-order inclusion techniques for the solution set of algebraic equations and state-of-the-art techniques for bounding the solution of nonlinear IDEs. We show how this approach can be used to bound the reachable set of uncertain semi-explicit DAEs by bounding the underlying IDEs. We demonstrate this approach on two case studies, a double pendulum where it proves superior with delayed break-down times compared to other methods, and anaerobic digestion of microalgae which has nine differential and two algebraic states. (C) 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
关键词	Implicit differential equations reachable set differential inequalities polynomial models ellipsoidal calculus high-order inclusions
出版地	PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
会议地点	Whistler, BC, Canada
收录类别	CPCI ; ISSHP ; EI
语种	英语
WOS记录号	WOS:000375842300017
出版者	ELSEVIER SCIENCE BV
EI入藏号	20160301805535
EI主题词	Algebra ; Anaerobic digestion ; Calculations ; Continuous time systems ; Differential equations ; Differentiation (calculus) ; Enclosures ; Equations of state ; Fault detection ; Nonlinear equations ; Pendulums
EI分类号	Mathematics:921 ; Systems Science:961
WOS关键词	ALGEBRAIC EQUATIONS ; VALIDATED SOLUTIONS ; SYSTEMS ; INDEX
原始文献类型	Proceedings Paper
引用统计
文献类型	会议论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/2292
专题	信息科学与技术学院_PI研究组_Boris Houska组
通讯作者	Rayjaguru, Jai
作者单位	1.Univ London Imperial Coll Sci Technol & Med, Ctr Proc Syst Engn, Dept Chem Engn, South Kensington Campus, London SW7 2AZ, England 2.ShanghaiTech Univ, Sch Informat Sci & Technol, Shanghai 200031, Peoples R China
推荐引用方式 GB/T 7714	Rayjaguru, Jai,Villanueva, Mario E.,Houska, Boris,et al. Continuous-Time Enclosures for Uncertain Implicit Differential Equations[C]. PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS:ELSEVIER SCIENCE BV,2015:94-99.